Solution - Simplification or other simple results
Other Ways to Solve:
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((0 - 3x2) - 22x) - 24
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
-3x2 - 22x - 24 = -1 • (3x2 + 22x + 24)
Trying to factor by splitting the middle term
3.2 Factoring 3x2 + 22x + 24
The first term is, 3x2 its coefficient is 3 .
The middle term is, +22x its coefficient is 22 .
The last term, "the constant", is +24
Step-1 : Multiply the coefficient of the first term by the constant 3 • 24 = 72
Step-2 : Find two factors of 72 whose sum equals the coefficient of the middle term, which is 22 .
| -72 | + | -1 | = | -73 | ||
| -36 | + | -2 | = | -38 | ||
| -24 | + | -3 | = | -27 | ||
| -18 | + | -4 | = | -22 | ||
| -12 | + | -6 | = | -18 | ||
| -9 | + | -8 | = | -17 | ||
| -8 | + | -9 | = | -17 | ||
| -6 | + | -12 | = | -18 | ||
| -4 | + | -18 | = | -22 | ||
| -3 | + | -24 | = | -27 | ||
| -2 | + | -36 | = | -38 | ||
| -1 | + | -72 | = | -73 | ||
| 1 | + | 72 | = | 73 | ||
| 2 | + | 36 | = | 38 | ||
| 3 | + | 24 | = | 27 | ||
| 4 | + | 18 | = | 22 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 18
3x2 + 4x + 18x + 24
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (3x+4)
Add up the last 2 terms, pulling out common factors :
6 • (3x+4)
Step-5 : Add up the four terms of step 4 :
(x+6) • (3x+4)
Which is the desired factorization
Final result :
(-3x - 4) • (x + 6)
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